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AS Level · Mechanics 1 WME01

Quantities, Units & Modelling

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Edexcel IAL · Mechanics 1

Quantities, Units & Modelling

Every mechanics problem describes the real world with numbers that have both size and direction — measured in agreed units — and simplified by smart assumptions.

5 Topics Covered 10 Practice Questions Answers Hidden Until You Click Works Offline

Chapter Overview

Scalars vs Vectors — Some quantities have direction (vectors), others don't (scalars). This distinction changes how you add and work with them.
Fundamental SI Units — Length in metres (m), time in seconds (s), mass in kilograms (kg). All other units build from these.
Derived Units — Speed, acceleration, and force are combinations of SI units. You can always reconstruct a formula from its units.
Types of Force — Weight, tension, thrust, friction, and normal reaction. Each acts in a specific, predictable direction.
Modelling Assumptions — We simplify real life (smooth surfaces, light strings, particles) so the maths stays solvable.

Scalars & Vectors

What is the difference?

Think of it this way: if someone tells you a car is going 60 km/h, you know its speed — but you don't know whether it's heading toward you or away from you. That's a scalar. If they say 60 km/h due north, now you know everything you need — that's a vector.

The key test: does the quantity need a direction to be fully described? If yes → vector. If no → scalar.

⬤ Scalar

Magnitude only. Always positive.

Speed · Distance · Time · Mass · Temperature

⬤ Vector

Magnitude + Direction. Can be negative.

Velocity · Displacement · Acceleration · Force · Momentum

Speed vs Velocity: A car going at 30 m/s and braking has scalar speed of 30 m/s, but its velocity might be +30 m/s (forward) or −30 m/s (in the negative direction). Velocity gives you direction; speed doesn't.

In writing: Vectors are shown in bold non-italic font in textbooks (e.g. F, a). In your handwriting, you must underline them (e.g. F, a). Don't forget this in exams!

Key Definitions

Displacement — Distance moved in a given direction from a starting point (vector).

Velocity — Speed in a given direction = displacement ÷ time (vector).

Acceleration — Rate of change of velocity (how quickly velocity changes) (vector).

Worked Example

Classify each as scalar or vector:
a) A speedboat travels at 3 m/s on bearing 052° b) A garden is 1.7 m wide
c) A car accelerates at 5.4 ms⁻² d) A film lasts 2 h 17 min
e) An athlete runs at 10.44 ms⁻¹ average speed f) A ball rolls forwards 60 cm

VECTOR — A speed with a direction given (bearing) = velocity.

SCALAR — A length with no direction stated.

VECTOR — Acceleration always has direction.

SCALAR — Time has no direction.

SCALAR — It says "speed" with no direction — that's scalar.

VECTOR — "Forwards" gives a direction, making this displacement.

Practice Question 1

A runner completes a 400 m race and returns to the start. State the runner's total distance and total displacement, explaining the difference.

Practice Question 2

Fundamental (SI) Units

The three units that rule them all

Système International

Length / Displacement

Metres

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Also in the full note

What to Memorise
Concepts Checklist
Exam Tips & Common Mistakes
Conversion facts you must know
Building units from m, s, kg
What is a force?
Why do we simplify?

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Quantities, Units & Modelling

Quantities, Units & Modelling

Chapter Overview

Scalars & Vectors

What is the difference?

Fundamental (SI) Units

The three units that rule them all

More Mechanics 1 topics